Transplant recipients have accessed the memories and emotions of the donors, so there is hard science behind the your question.
We will of course, one day, be able to create organs based on the patient’s DNA. If memory/emotions are stored holographically in the body, then those memories and emotions “could/should/would” repopulate an organ with the same DNA, but it it would probably take awhile–we have zero data on this. But it’s more likely that instead of growing and transplanting whole organs, the same genetic technologies would allow us to repair the organs, there should be no loss of memory/emotions at all. This is a classic Ship of Theseus situation
As for losing a piece of ourselves, our souls , or just something integral, that seems obvious that we lose something. Lifeforce takes a hit from a major surgery, but there is an underlying pattern in each of us. I’ve always been impressed by the phantom leaf effect and the aforementioned donor “memories” that are accessible to the recipient are very suggestive.
I suspect with donated organs, the original donor memories fade over time, but I will research this, as it is fascinating…
Overall, I wouldn’t be too concerned. I can’t spell out doctrine, but I think that our purpose here is not derailed by losing an organ or a limb, though it is inconvenienced to be sure, which is why genetic engineering can be an important tool to alleviate suffering.
Soon I will get the robust organs field. Your post is a good reminder.